The present patent document claims priority to German Application Ser. No. DE 10207623.5, filed Feb. 22, 2002, which is hereby incorporated by reference.
1. Field
The invention relates to a method for performing computer tomography, having the following method steps: for scanning an object by means of a cone-shaped beam exiting from a focal point and by means of a matrix-like detector array for detecting the beam, the focal point is moved in relation to the object on a spiral path about a system axis, and the detector array provides output data corresponding to the received radiation; and from output data furnished during the motion of the focal point on a spiral segment, images of an object region executing a periodic motion are reconstructed, taking into account a signal, obtained in the course of the periodic motion, which reproduces the course over time of the periodic signal. The invention furthermore relates to a computed tomography (CT) apparatus, having a radiation source, from whose focal point a cone-shaped beam is emitted; a matrix-like detector array for detecting the beam, the detector array providing output data corresponding to the received radiation; a device for generating a relative motion between the radiation source and the detector array on the one hand and an object on the other; and an image computer to which the output data is supplied, and a device for creating a relative motion for scanning the object by the beam and the two-dimensional detector array caused by a relative motion of the focal point in respect to a system axis in such a way that the focal point moves on a helical spiral path in relation to the system axis, whose center axis corresponds to the system axis; and where the image computer reconstructs images of an object region executing a periodic motion from output data furnished during the motion of the focal point on a spiral segment while taking a signal into account, which reproduces the course over time of the periodic motion and which was obtained during the scanning process with the aid of an appropriate device.
2. Background
A method and a CT apparatus of this kind are known from DE 198 42 238 Al. This method is disadvantageously suitable only for detector arrays which extend a relatively short distance in the direction of the system axis.
Various CT methods using cone-shaped X-ray beams have become known, in particular in connection with detector arrays having several rows of detector elements. In them, the cone angle that is due to the cone-shaped form of the X-ray beam is taken into account in various ways.
In the simplest case (see, for example, K. Taguchi, H. Aradate in xe2x80x9cAlgorithm for Image Reconstruction in Multi-Slice Helical CTsxe2x80x9d, Med. Phys. 25, pp. 550 to 561, 1988, or H. Hu in xe2x80x9cMulti-Slice Helical CT: Scan and Reconstructionxe2x80x9d, Med. Phys. 26, pp. 5 to 18, 1999), the cone angle is ignored, which has the disadvantage that with a large number of rows, and therefore a large cone angle, artifacts appear.
Moreover, the so-called MFR algorithm (S. Schaller, T. Flohr, P. Steffen in xe2x80x9cNew efficient Fourier reconstruction method for approximate image reconstruction in spiral cone-beam CT at small cone anglesxe2x80x9d, SPIE Medical Imaging Conf. Proc., Vol. 3032, pp. 213 to 224, 1997) has become known, but it is disadvantageous because an elaborate Fourier reconstruction is required, and the image quality leaves something to be desired.
Exact algorithms have furthermore been described (for example by S. Schaller, F. Noo, F. Sauer, K. C. Tam, G. Lauritsch, T. Flohr in xe2x80x9cExact Radon Rebinning Algorithm for the Long Object Problem in Helical Cone-Beam CTxe2x80x9d, Proc. of the 1999 Int. Meeting on Fully 3D Image Reconstruction, pp. 11 to 14, 1999, or H. Kudo, F. Noo and M. Defrise in xe2x80x9cCone-Beam Filtered Backprojection Algorithm for Truncated Helical Dataxe2x80x9d, Phys. Med. Biol. 43, pp. 2885 to 2909, 1998), which have the disadvantage of an extremely elaborate reconstruction in common.
Another such method and CT apparatus are known from U.S. Pat. No. 5,802,134. In this reference, however, images are reconstructed for image planes which are inclined by an inclination angle xcfx84 about the x-axis relative to the system axis z. By this device, the at least theoretical advantage is achieved that the images contain fewer artifacts if the angle of inclination xcfx84 has been selected to be such that a good adaptation, if possible in accordance with a suitable error criterion, such as the minimum mean square value of the distance of all points of the spiral segment from the image plane, measured in the z-direction, and even an optimal adaptation of the image plane to the spiral path is provided.
In this case, the spiral path of the focal point F illustrated in FIG. 1 is described by the following equations:                               x          f                =                              -                          R              f                                ⁢          cos          ⁢                      xe2x80x83                    ⁢          α                                    (        1        )                                          y          f                =                              -                          R              f                                ⁢          sin          ⁢                      xe2x80x83                    ⁢          α                                    xe2x80x83                                          z          f                =                              S            ·            p            ·                          α                              2                ⁢                π                                              ⁢                      xe2x80x83                    ⁢          or                                    xe2x80x83                                                      x            _                    f                =                  (                                                                                          -                                          R                      f                                                        ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                  α                                                                                                                          -                                          R                      f                                                        ⁢                  sin                  ⁢                                      xe2x80x83                                    ⁢                  α                                                                                                      Sp                  ⁢                                      α                                          2                      ⁢                      π                                                                                                    )                                    xe2x80x83            
In the case where the detector elements of the detector array are arranged in rows extending transversely to the system axis Z and in columns extending parallel to the system axis Z, S stands for the length of one detector row in the direction of the system axis, and p stands for the pitch, where p=h/S, and h stands for the slope of the spiral path per revolution of the focal point F. xcex1 is the projection angle, and an image plane will now be addressed that belongs to data that was acquired over a projection angle range of xc2x1xcex1; the reference projection associated with this image plane is at xcex1r=0, and thus represents the center of the projection angle range xc2x1xcex1. Below, xcex1r will be called the reference projection angle.
In the conventional spiral CT, so-called transverse section images are reconstructed, that is, images for image planes that are perpendicular to the system axis marked z and that thus include both the x-axis and the y-axis; the x- and y-axes are perpendicular to one another and to the system axis z.
In the case of U.S. Pat. No. 5,802,134, conversely, images are reconstructed for image planes that are inclined by an angle of inclination xcex3 about the x-axis to the system axis z, as shown in FIG. 2. As a result, the at least theoretical advantage is attained that the images contain fewer artifacts if the angle of inclination xcex3 is selected such that there is a good optimal adaptation of the image plane to the spiral path, if at all possible in accordance with a suitable error criterion, such as a minimum mean square value of the distance, measured in the z-direction, of all points in the spiral segment from the image plane.
In the case of U.S. Pat. No. 5,802,134, fan beam data, that is, data acquired using fan beam geometry, which is known per se, and obtained in the motion of the focal point over a spiral segment whose length was 180xc2x0 plus the fan or cone angle, such as 240xc2x0, are used for the reconstruction. Referred to the reference projection angle, xcex1r=0, the applicable equation for the normal vector of the image plane is                     n        _            ijs        ⁡          (      γ      )        =            (                                    0                                                                              -                sin                            ⁢                              xe2x80x83                            ⁢              γ                                                                          cos              ⁢                              xe2x80x83                            ⁢              γ                                          )        .  
The optimal angle of inclination xcex3 is evidently dependent on the slope of the spiral and thus on the pitch p.
In principle, the method known from U.S. Pat. No. 5,802,134 can be employed for arbitrary values of the pitch p. However, below the maximum pitch pmax, optimal utilization of the available detector area and thus of the radiation dose delivered to the patient to obtain images (detector and hence dose utilization) is not possible, because even though a given transverse slice, that is, a slice of the object that is perpendicular to the system axis a, is scanned over a spiral segment that is longer than 180xc2x0 plus the fan or cone angle, still in the method known from U.S. Pat. No. 5,802,134, for values of the pitch p below the maximum pitch pmax, only a spiral segment whose length is 180xc2x0 plus the cone angle can be used, since using a longer spiral segment would make it impossible to adapt the image plane well enough to the spiral segment.
The object is to embody a method and a CT apparatus such that it is also suitable for detector arrays with a great length in the direction of the system axis, and that accordingly makes high-quality images possible. Images with an inclined image plane are reconstructed from output data furnished during the motion of the focal point on a spiral segment; the image planes of these images are inclined relative to the system axis both about a first axis, which perpendicularly intersects the system axis, by an angle of inclination xcex3 and about a second axis, which perpendicularly intersects both the first axis and the system axis, by a tilt angle xcex4.
As a result, even at pitch values that are below the maximum pitch, it is possible to achieve at least approximately complete detector and dose utilization.
Since a signal that reproduces the course over time of the periodic motion is obtained, and the spiral segments are to be selected such that they correspond to a phase of the periodic motion that is to be imaged, the reconstruction of high-quality images is assured,
In the simplest case of one variation, the images with an inclined image plane are reconstructed from output data that belong to a spiral segment which originates in a single cycle, i.e., a single period, of the periodic motion.
If the chronological resolution achievable with output data originating in a single cycle of the periodic motion is inadequate, then a variant aspect provides that the images with an inclined image plane from a spiral segment that is composed of output data that originate in a plurality of preferably immediately successive cycles of the periodic motion are reconstructed. In an embodiment, it may be provided that the output data of which the spiral segment is composed originate in subsegments of equal length. For instance, in the case of two subsegments in the first of the two cycles, a subsegment is selected that is in phase with the phase to be imaged of the periodic motion. In the next cycle, a subsegment is determined that is complementary to the first subsegment and, with it, forms a spiral segment, and that has the least possible chronological spacing from the phase to be imaged of the periodic motion.
Alternatively, the output data of which the spiral segment is composed can originate in subsegments of unequal length, each of which is disposed symmetrically to a reference time of the periodic motion. In that case, both subsegments are selected to be in phase with the phase to be imaged of the periodic motion.
To make unambiguous definition of the reference time possible, a variant embodiment provides that this reference time in each case is later than the onset of one period of the periodic motion by a length of time that is equivalent to an adjustable fraction of the period length of the periodic motion. To compensate for fluctuations in the period length, mean period lengths of the periodic motion can be used.
In a first alternative embodiment with regard to the image reconstruction, for a given pitch p and a given z-position zima, output data for a total segment of length [xe2x88x92xcex1max, +xcex1max] are obtained, in which xcex1max=Mxcfx80/p, and M is the number of detector rows. This total segment is subdivided into a number nima of spiral segments that overlap one another, each of which has the length of 180xc2x0 plus the cone angle. For each of the spiral segments, its own image with an inclined image plane is reconstructed at the point zima. By the reconstruction of an image with an inclined image plane for each of the spiral segments, it is possible, by a suitable choice of the angle of inclination xcex3 and the tilt angle xcex4, to adapt the image plane of the image for each of these spiral segments optimally to the corresponding portion of the spiral segment and to utilize both the detector array and the dose theoretically completely and in practice as nearly completely as possible.
In an alternative second embodiment, on the basis of the output data obtained for a spiral segment, 180xc2x0 plus the cone angle in length, that is centered relative to the reference projection angle xcex1r=0, a number nima of images with a variously inclined image plane for various z-positions is reconstructed. By the reconstruction of a plurality of images with a variously inclined image plane for various z-positions, it is possible, by a suitable choice of the angle of inclination xcex3 and the tilt angle xcex4 to adapt the image plane of the image for each of these z-positions optimally to the spiral segment, and to utilize both the detector array and the dose theoretically completely and in practice as nearly completely as possible. In a preferred embodiment, the plurality of inclined image planes intersect on a straight line that extends at a tangent to the spiral.
To obtain the most complete possible detector and dose utilization, in a variant aspect for the extreme values +xcex4max and xe2x88x92xcex4max of the tilt angle xcex4 of the inclined image planes belonging to one spiral segment, the following equation applies:       ±          δ      min        =      arctan    ⁡          (                                    -                          SM              2                                +                                    Sp              ⁢                                                α                  i                                                  2                  ⁢                  π                                                      ±                          RF0V              ⁢                              xe2x80x83                            ⁢              cos              ⁢                              xe2x80x83                            ⁢                              α                i                            ⁢              tan              ⁢                              xe2x80x83                            ⁢                              γ                0                                                                          -                                          R                f                                            cos                ⁢                                  xe2x80x83                                ⁢                                  γ                  0                                                              -                                    (                              ±                RF0Y                            )                        ⁢                                          sin                ⁢                                  xe2x80x83                                ⁢                                  α                  i                                                            cos                ⁢                                  xe2x80x83                                ⁢                                  γ                  0                                                                        )      
in which xcex30 is the value, averaged for the tilt angle xcex4=0 in accordance with the equation       γ    0    =      tan    ⁡          (                                    -            sp                    ⁢                      α            ^                                    2          ⁢          π          ⁢                      xe2x80x83                    ⁢                      R            f                    ⁢          sin          ⁢                      α            ^                              )      
of the angle of inclination xcex3.
For the sake of high image quality, in a further variant aspect is provided that for a given amount |xcex4max| of the maximum value for the tilt angle xcex4, the associated optimal value xcex3min of the angle of inclination xcex3 is ascertained such that an error criterion, such as a minimum mean square value of the distance, measured in the z-direction, of all the points on the spiral segment from the image plane, is met.
If the axis of rotation about which the focal point rotates about the system axis is not identical to the system axis but instead intersects the system axis at a gantry angle xcfx81, then for the angle of inclination xcex3xe2x80x2 to be selected, the following equation applies:       γ    xe2x80x2    =      arctan    ⁢                            Sp          ·          cos                ⁢                  xe2x80x83                ⁢        ρ                                          4            ⁢                                          π                2                            ·                              R                f                                              +                                    S              2                        ⁢                          p              2                                +                      4            ⁢                          π              ·                              R                l                                      ⁢            cos            ⁢                          xe2x80x83                        ⁢            α            ⁢                          xe2x80x83                        ⁢            sin            ⁢                          xe2x80x83                        ⁢                          ρ              ·              Sp                                          
Once again, for a given amount of the maximum value for the tilt angle |xcex4max|, the possibility exists of ascertaining the associated optimal value of the angle of inclination xcex3xe2x80x2 such that an error criterion, such as a minimum square value of the distances, measured in the z-direction, of all the points on the spiral segment from the image plane, is met.
To achieve the most complete possible detector and dose utilization, in a variant of embodiment, for the number nima of inclined image planes for which images with an inclined image plane are generated for each spiral segment, the following equation also applies:       n    ima    =      floor    ⁡          [              sM        p            ]      
Also for the sake of the most complete possible detector and dose utilization, on the condition that the detector rows are of equal width, in a variant of the embodiment, the tilt angles xcex4 of the inclined image planes are ascertained in accordance with the equation       δ    ⁡          (      i      )        =            δ      max        ⁢                            2          ⁢          i                -                  (                                    n              ima                        -            1                    )                                      n          ima                -        1            
To obtain transverse section images, which the users of CT apparatuses are used to, in a variant of the embodiment, reformatting is provided; that is, in a further method act, a transverse section image is generated by combining a plurality of images with an inclined image plane. In one feature, the combining can be done by combining the plurality of images with an inclined image plane into a transverse section image by interpolation, or in particular by weighted averaging.
In combining a plurality of images with an inclined image plane into a transverse section image, it is also possible, in a preferred variant embodiment with a further method act, for the number of images with an inclined image plane that are combined in order to generate a transverse section image to be selected in accordance with whatever slice thickness of the transverse slice is desired. For the sake of the highest possible image quality of the transverse section images, it is also possible for the images with an inclined image plane having the least possible slice thickness to be reconstructed.
A desired slice thickness of the transverse slice represented in a transverse section image can be established, in a further preferred variant, in that the number of images with an inclined image plane that are combined to generate a transverse section image is selected in accordance with the equation
NM=2xc2x7max(z*,sup"PHgr"xcex94zR)/Sxc2x7NS
The CT apparatus operating as described herein has similar advantages and features as the methods described above. Exemplary embodiments of the invention are described below in conjunction with the drawings.